Magnetically assisted soft milli-tools for occluded lumen morphology detection

Methodologies based on intravascular imaging have revolutionized the diagnosis and treatment of endovascular diseases. However, current methods are limited in detecting, i.e., visualizing and crossing, complicated occluded vessels. Therefore, we propose a miniature soft tool comprising a magnet-assisted active deformation segment (ADS) and a fluid drag-driven segment (FDS) to visualize and cross the occlusions with various morphologies. First, via soft-bodied deformation and interaction, the ADS could visualize the structure details of partial occlusions with features as small as 0.5 millimeters. Then, by leveraging the fluidic drag from the pulsatile flow, the FDS could automatically detect an entry point selectively from severe occlusions with complicated microchannels whose diameters are down to 0.2 millimeters. The functions have been validated in both biologically relevant phantoms and organs ex vivo. This soft tool could help enhance the efficacy of minimally invasive medicine for the diagnosis and treatment of occlusions in various circulatory systems.


Supplementary Note S1. Physiological features of the possible occlusions
Vascular occlusion can occur in various parts of the body (76)(77)(78)(79)(80)(81)(82). Here, we used the coronary artery as a reference for the design and fabrication of simulants. The diameter of the coronary artery is in the range of 2 -4 mm (83,84), and we chose 3.0 mm as the normal diameter n of the uniform size lumen of the simulants. For the simulants of partial occlusions, we used vascular stenosis as a reference. The partial occluded vessels could be accompanied by complex internal structures, e.g., diffuse stenosis (77,85,86), which may be caused by the presence of diffused small plaques. We set the length of occlusions o to 20.0 mm, which is within the range of the stenosis length (87,88). For the simulants of severe occlusions, we chose CTO as a reference and mainly considering the minimum diameter c_min of the internal MC, which is usually less than 0.5 mm and has a cross-sectional area mc of up to 2.4 mm 2 (89,90). CTO could be on main branches, and on side branches with acute or obtuse bifurcation angles (91). MCs inside CTO are complex structures, they could be tortuous and have multiple points extending to various locations, e.g., vessel walls, the distal end of the vessel, and even stopping in the middle (false MC) (92)(93)(94)(95).
In our investigations and demonstrations, we utilized the CTO with the blunt type entrance as the reference, which is more difficult to detect and access than the tapered entrance clinically (96)(97)(98)(99).
The minimum allowed distance between the magnet and the lumen z_min varies for different organs, tissues, and imaging views given the physical constraints (63)(64)(65). For example, the distance between the skin and the heart varies depending on the imaging view used, e.g., 32.1 ± 7.9 mm for parasternal, 31.3 ± 11.3 mm for apical, and 70.8 ± 22.3 mm for subcostal (65). In our investigation, we investigated the effects of the distance z between the magnet and the lumen on the tool's performance in the range of 20 mm to 140 mm, and in demonstrations, we maintained the distance z in the range of 40 to 100 mm. For visualizing the morphology of partial occlusion, we set the imaging parameters of the X-ray to 50 kV and 65 μA, which are consistent with the range of parameters used for medical X-ray imaging (100)(101)(102)(103)(104). In the clinic, the injection speed of the medical contrast agent is in the range of 0.5 -5.0 ml/s (105)(106)(107). In demonstrations, we maintained the injection speed of the contrast agent simulant, i.e., dissolved food dye, and medical contrast agent in the range of 0.4 -1.2 ml/s. There is also a correlation between the flow rate in narrowed vessels and the degree of occlusions. of the partial occlusion, i.e., mild, moderate, and severe stenosis, is usually in the range of 10.0 -70.0 ml/min and basically decreases as the grade of the stenosis increases (62,84).
While for severe occlusions, i.e., CTO, the is no more than 10.0 ml/min (90,108). Considering the body healthy state, the viscosity of the blood could be changed in the range of 4 -45 cP (109), we investigated the performance of the tool in the range of 0.9 -50.0 cP. The average resting heart rate for adults ranges from 60 to 100 bpm, and we unified the rate to 80 bpm. We used a commercial pulsatile blood pump (Harvard Apparatus) to pump blood analog with 80 bpm in all the experimental conditions with the flow.

Supplementary Note S2. Modeling of the deformation of the ADS
Here, we utilized the pseudo-rigid-body (PRB) model and the energy-based approach to model and solve the kinematics of the active deformation segment (ADS) with multi-mode deformation (75). For a PRB model, it was assumed that the rod comprises N rigid links jointed by N-1 flexible joints. In this study, as all large bending deformation of the ABS occurred in bending sections as shown in fig. S26, we considered the bending sections of ADS as the flexible joints and adjacent magnetization segments of the joint to be two magnetic rods with opposite magnetization directions. Besides, we assumed that each joint has one degree of freedom for bending, which ignored the extension, shear, and twisting of the rod. Thus, rod kinematics could be described as the poses of the discrete links along with the arc length.

Elastic energy E
As shown in fig. S26, the length of the joint could be calculated by: where ADS was the thickness of ADS (in direction).
The rotation angle of a single rod relative to axis could be described by the angle i , which means that we could know the strain i of the th joints, as follows: Therefore, in the final state, we could know the elastic energy stored in the ADS was where ADS and ADS were Young's modulus and the area moment of inertia of ADS, respectively.

Magnetic energy U
As we know the deformation of a single rod relative to the axis, we could know the direction vector for the th rod was i r = (cos( i ) , sin( i )).
Furthermore, the vector from the zero point to the end point of the th rod was where m was the length of the rod, which was equal to the length of one magnetization segment of the ADS. Therefore, we could know the location of the end point of the th rod, which was i e .
And the vector from the zero point to the middle point of the ℎ rod was: Therefore, we could know the location of the middle point of the th rod, which was i m .
At the same time, as we know the direction vector for the th magnetized section, we could know the dipole moment d i for the th rod was: where d was the magnetic moment of one magnetization segment of the ADS. Since we know the location of the actuator magnet a ( mag , mag ), the magnetic energy of all rods in the pointdipole field could be calculated by: where ( i m ) was the magnetic field of the actuation magnet at the middle point of the th rod ( i m ). As the cubic actuator magnet (50 mm) was much larger than the ADS, we considered the magnetic field of the actuator magnet to be uniform in the direction and only change in the direction. We measured the magnetic field of the actuator magnet in different positions with a Gaussian meter, as shown in table S6.

Work done by the fluid drag W
We considered the blood analogue as the laminar flow and came from drag forces applied to the FDS and ADS. As we know the flow rate pumped into the inlet, we could know the average velocity of the blood analog in the lumen was: where lumen was the cross-section area of the lumen in the plane as shown in fig. S27.
Moreover, the velocity profile of the blood analogue relative to the beams of the FDS in plane could be calculated by (110): where was the radius of the lumen, d was the delivery speed of the tool.
We considered the tool always in the central area of the plane as it's a symmetric structure, and the length of the intermediate beam of the FDS in the direction was 0 as it's much smaller than the length b (in the direction) of the beams. The location of the FDS in the plane was (0, 0 ). Therefore, for one beam with the width b (in the direction), the drag force applied on it in the direction was: where b was the mass density of the blood analog and d was the drag coefficient. When the beam was placed vertically in low Reynolds number ( ) flow, the drag coefficient d changes rapidly with the flow speed changes (111)(112)(113), and given the results of (112), we could calculate drag coefficient d by: where was the viscosity of the blood analog, was the radius of the lumen.
Therefore, the flow drag applied on FDS Drag FDS was (10 ⋅ Drag b , 0).
When the ADS was placed in the lumen and deformed by the actuator magnet, we assumed that the fluid drag Drag i ( Drag i , 0) applied on the rods of the ADS remains constant, and the tool always in the central area of the lumen. Therefore, the fluid drag applied on the th rod was: Here, we considered = 2 ⋅ ( avg − d ) to be the maximum flow speed of the blood analogue in the lumen, as the rod, whose width was much less than the diameter of the lumen, was in the central area of the lumen. And ′ was the reference area of the rod in the lumen in the final state and could be calculated by where ADS was the width of ADS.
As we know the location of the rods, for the th rod, we could know the displacement of the middle point of it in the final state, which was: where N e 0 and N e was the position of the end point of the last rod in the initial and final states, respectively.
Furthermore, the work done by the fluid drag during the deformation was Since we have known the elastic energy and magnetic energy of the deformed ADS in the final state and the work done by the fluid drag applied on the tool. In order to obtain the rotation angle i , a static equilibrium configuration could be solved by finding the local minimum of the total potential energy The equilibrium equation could be solved by the fmincon solver in MATLAB (R2021b, MathWorks, Inc.), which was used to find the minimum of the constrained nonlinear multivariable function. Given the results solved, the maximum deformation height of ADS could be calculated by: where ℎ i was the deformation height for the th rod and could be calculated by

Supplementary Note S3. Floating and advancement of the tool
Here, we considered the tool to be rigid and composed of ADS, FDS, connection segment 1 (C1), and connection segment 2 (C2). When the tool was in the lumen, as the existence of gravity, buoyancy and fluid drag, there were three torques, generated by gravity ( g ), buoyancy ( b ), and fluid drag ( drag ), applied on the tool as shown in fig. S28. Those torques could lead to the rotation of the tool around the connection point c in the plane.
According to the experimental observation, the failure of advancement was caused by the buckling of the tool in contact with the luminal wall. Therefore, for successfully advancing and floating in occlusions, a torque was required to guide the tool rotating toward the center of the lumen to avoid contact with the wall.
We considered the FDS as a mass point. Given the geometric constraints ( fig. S27), the initial position of FDS in the plane could be calculated by
The torque generated by the FDS was where FDS and FDS were the mass density and volume of the FDS, respectively. was the gravitational acceleration. was the angle between the tool and the direction in the initial state and could be calculated by Besides, the torques, generated by the gravity, on the ADS, C1, C2 was respectively. Here, PDMS and ADS was the mass density of PDMS and ADS, respectively.
Thus, we could know that the torque generated by gravity and applied on the tool was: and the direction of g was clockwise.

Torque ( ) generated by buoyancy
As the four parts of the tool were under buoyancy in the fluid, b also was generated from four respectively.
Thus, we could know that the torque generated by the buoyancy was: and the direction of b was counterclockwise.

Torque ( ) generated by the drag force
When the lumen existed the flow, there would be a drag force parallel to the flow direction applied on the tool.
The drag applied on the C1, ADS, C2 and FDS was respectively.
Furthermore, the torque generated by the drag force applied on four parts was respectively.
Thus, the torque generated by the fluid drag and applied on the tool was and the direction of Drag was counterclockwise.
In our tests, for successful floating and advancement, the rotation direction of the tool should be counterclockwise. Hence, if the total torque total applied on the tool was written as the total torque applied on the tool should satisfy total > 0.
Since g and b were decided by the design of the tool, Drag was related to the flow rate and delivery speed d . Therefore, we could define a threshold of the torque Here, if  (114), the microparticles could be coated with various biocompatible materials such as silica (56), polyethylene glycol or dextran.
PDMS and Dragon Skin™ 30 polymer matrix have good safety and biocompatibility, which have been proven in vivo (58,115). However, PMDS is not hemocompatible due to the fast adsorption of proteins and relatively high adhesion of blood platelets, which would induce thrombosis (116). To improve the hemocompatibility of PDMS, surface modifications can be carried out to reduce its protein adsorption and platelet adhesion.
To further enhance the safety, i.e., biocompatibility and hemocompatibility of the tool, we coated a layer of dimethylacrylamide (DMAA) hydrogel on its surface. DMAA-based hydrogel has been shown to have low levels of hemolysis, platelet adhesion, and minimal activation of coagulation and complement, making it a suitable choice for blood-contact applications. However, further research and validation are needed to ensure its safety in practical applications, particularly in the in vivo environment (56).

Supplementary Note S5. Safety interaction with vessels
When the ADS was deformed by the magnet and the tool was retracted, there were two groups of interaction forces, i.e., the radial forces ( r b_wall and r u_wall ), and the axial forces ( f b_wall and f u_wall ), applied on the wall of the lumen, as shown in fig. S23A.
Actuated by the magnet, the deformed ADS would contact the wall of the lumen on several contact points. We assumed that all external forces are uniformly distributed on each magnetized segment of deformed ADS and selected one of the magnetized segments for analysis. When the wall was compressed by the deformed ADS, 1) the radial forces from two sources: the magnetic force and magnetic torque applied to the magnetization segments of the deformed ADS. For each magnetization segment, within the range of the distance z between the magnet and ADS we investigated (20 -100 mm), the radial action force due to the magnetic force was no more than                   The pulsatile flow rate Q into the inlet was set to around 20.0 ml/min. Scale bar: 3 mm.                Mov. S1. Visualization of a complicated partial occlusion.